How to make female's stocking as tight fit
The way to get the one mesh to snap to the other is to use Blenders snapping tools. The controls for this are located at the bottom of the 3D view on the right side of the row of icons just before the OpenGL render buttons.

There is a magnet icon, a small menu with a few options, and then numerous other options based on your menu choice. You will want to set the menu to face instead of increment. All of the other settings should be fine.

Now, when you select a section of your mesh and move it, if you hold Ctrl while you move it it will snap to whatever face from another object is under your mouse. The little magnet icon can be clicked to automatically snap without holding Ctrl if that is easier for you. Snapping also works when you move something on a single axis only or two axes. I your case you may want to try pressing Shift+Z while moving the vertices so that you don't mess up the vertical placement while snapping.